The calculation and design of geometric parameters of a double-circular-arc gear-shaper cutter and the analysis of its tooth profile error are one of the challenges in harmonic drive manufacturing. In order to study the calculation method of geometric parameters and the distribution of tooth profile errors, a mathematical model of the tooth profile and tooth surface of the double-circular-arc gear-shaper cutter is established by kinematics method. Based on the model, the influence of the back angle of the top edge of double-circular-arc gear-shaper cutter on the grindable length of the gear-shaper cutter is studied; the calculation methods of the geometric parameters, such as the back angle of the side edge and the front angle of the side edge, are put forward, and the influential factors of these parameters and the change law from the top of the tooth to the root of the tooth are studied; the influence of the front angle and the back angle of the top edge on the tooth profile error of the double-circular-arc gear-shaper cutter is analyzed; and the design method of the rake angle of the gear-shaper cutter is given by an example. The conclusions are drawn as follows. 1) The grindable length of the gear-shaper cutter decreases with the increase of the back angle of the top edge. 2) The back angle of the side edge is related to the radius of the point and the pressure angle and increases with the increase of the back angle of the top edge. 3) The front angle of the side edge increases with the increase of the front angle of the top edge and the back angle of the top edge, and the front angle of the top edge has a greater influence on the front angle of the side edge. 4) Both the front angle and the back angle of the top edge have a great influence on the tooth shape error of the gear shaper. In short, when selecting the parameters, a larger front angle and a smaller back angle should be selected under the condition of ensuring the accuracy of tooth profile.